Rquot

Rquot is a statistical framework for robust quotient estimation, designed to compute a quotient of two dependent measurements in a way that minimizes sensitivity to outliers and measurement error. It provides estimators for the typical ratio E[Y]/E[X] or for the central tendency of the ratio Y/X when X and Y are observed with noise and possible correlation.

Origin and naming: The term Rquot arose in robust statistics literature in the early 2010s, as researchers sought ratio estimators with strong outlier resistance. The name reflects its focus on quotients and its emphasis on robustness. It has since been formalized in methodological work and implemented in statistical software.

Methodology: The Rquot estimator uses a robust loss function, such as Huber or Tukey, applied to the quotient Y/X or to a log-transformed form to stabilize variance. An iterative reweighted least squares (IRLS) procedure is typically employed to jointly estimate the ratio r while accounting for the covariance between X and Y. The method can handle heteroscedasticity and some dependence between numerator and denominator, and it provides standard errors via bootstrap or the delta method.

Applications: Rquot is used in pharmacokinetics for drug concentration ratios, in finance for robust pricing or earnings-type ratios, in environmental science for pollutant concentration ratios, and in engineering when ratio estimates are central but data quality is variable. It includes strategies for dealing with zero denominators, such as small offsets or joint distribution modeling.

Implementation: Several statistical tools offer Rquot implementations, including packages for R and Python. Typical workflows involve selecting a robust loss, fitting the IRLS model, and reporting the ratio estimate with confidence intervals and sensitivity analyses.

See also: robust statistics, ratio estimator, bootstrap, delta method, outlier detection.